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New Advances in Functional Analysis
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New Advances in Functional Analysis

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Computational and Applied Mathematics".

Deadline for manuscript submissions: closed (26 August 2022) | Viewed by 8174

Special Issue Editors

Prof. Dr. Lu-Chuan Ceng

E-Mail Website
Guest Editor
Department of Mathematics, Shanghai Normal University, Shanghai 200234, China
Interests: functional analysis; fixed point theory; applied convex analysis; nonlinear approximation theory in Banach space; variational inequalities; approximate solutions; general topology; applied nonlinear analysis
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Ching-Feng Wen

E-Mail Website
Guest Editor
Research Center for Nonlinear Analysis and Optimization, Kaohsiung Medical University, Kaohsiung 80708, Taiwan
Interests: fixed point theory; theory and algorithms on variational inequalities; set-valued and variational analysis; nonlinear analysis; optimization; well-posedness and optimal control
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Nowadays, functional analysis is a very important research field. In particular, as its branch, nonlinear functional analysis has played a crucial role in the exploration of various nonlinear phenomena in the real world. Results on solvability and numerical calculation solutions to the fixed-point equations of nonlinear operators exhibit the extraordinary versatility for applications in pure and applied sciences.

Nonlinear optimization also exhibits an extraordinary role in the exploration of some features that explain various nonlinear phenomena in the real world, such as efficiency, control, etc. Its research topics cover best approximation, numerical computation, efficiency solutions, well-posedness and so forth.

The objective of this Special Issue is to report new results in the two research areas as above: nonlinear functional analysis and optimization, and their applications. This Special Issue will accept high-quality papers including original research results, with illustrative applications, and survey articles of exceptional merit.

Prof. Dr. Luchuang Ceng
Prof. Dr. Ching-Feng Wen
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • Solvability of fixed-point equations of nonlinear operators
  • Best approximation problems in Banach spaces
  • Iterative procedures for fixed points or best proximity points
  • Nonlinear optimization and applications
  • Variational inclusions and equilibrium problems
  • Existence and optimality conditions
  • Dynamical systems and special functions
  • Well-posedness and optimal control

Published Papers (5 papers)

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Research

15 pages, 301 KiB  
Article
An Application to Fixed-Point Results in Tricomplex-Valued Metric Spaces Using Control Functions
by Rajagopalan Ramaswamy, Gunaseelan Mani, Arul Joseph Gnanaprakasam, Ola A. Ashour Abdelnaby and Stojan Radenović
Mathematics 2022, 10(18), 3344; https://0-doi-org.brum.beds.ac.uk/10.3390/math10183344 - 15 Sep 2022
Cited by 2 | Viewed by 891
Abstract
In the present work, we establish fixed-point results for a pair of mappings satisfying some contractive conditions on rational expressions with coefficients as point-dependent control functions in the setting of tricomplex-valued metric spaces. The proven results are extension and generalisation of some of [...] Read more.
In the present work, we establish fixed-point results for a pair of mappings satisfying some contractive conditions on rational expressions with coefficients as point-dependent control functions in the setting of tricomplex-valued metric spaces. The proven results are extension and generalisation of some of the literature’s well-known results. We also explore some of the applications to our key results. Full article
(This article belongs to the Special Issue New Advances in Functional Analysis)
17 pages, 595 KiB  
Article
Modified Iterative Schemes for a Fixed Point Problem and a Split Variational Inclusion Problem
by Mohammad Akram, Mohammad Dilshad, Arvind Kumar Rajpoot, Feeroz Babu, Rais Ahmad and Jen-Chih Yao
Mathematics 2022, 10(12), 2098; https://0-doi-org.brum.beds.ac.uk/10.3390/math10122098 - 16 Jun 2022
Cited by 8 | Viewed by 1226
Abstract
In this paper, we alter Wang’s new iterative method as well as apply it to find the common solution of fixed point problem (FPP) and split variational inclusion problem (SpVIP) in Hilbert space. We discuss the weak convergence for ( [...] Read more.
In this paper, we alter Wang’s new iterative method as well as apply it to find the common solution of fixed point problem (FPP) and split variational inclusion problem (SpVIP) in Hilbert space. We discuss the weak convergence for (SpVIP) and strong convergence for the common solution of (SpVIP) and (FPP) using appropriate assumptions. Some consequences of the proposed methods are studied. We compare our iterative schemes with other existing related schemes. Full article
(This article belongs to the Special Issue New Advances in Functional Analysis)
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29 pages, 1245 KiB  
Article
A New Construction and Convergence Analysis of Non-Monotonic Iterative Methods for Solving ρ-Demicontractive Fixed Point Problems and Variational Inequalities Involving Pseudomonotone Mapping
by Chainarong Khunpanuk, Bancha Panyanak and Nuttapol Pakkaranang
Mathematics 2022, 10(4), 623; https://0-doi-org.brum.beds.ac.uk/10.3390/math10040623 - 17 Feb 2022
Viewed by 1206
Abstract
Two new inertial-type extragradient methods are proposed to find a numerical common solution to the variational inequality problem involving a pseudomonotone and Lipschitz continuous operator, as well as the fixed point problem in real Hilbert spaces with a ρ-demicontractive mapping. These inertial-type [...] Read more.
Two new inertial-type extragradient methods are proposed to find a numerical common solution to the variational inequality problem involving a pseudomonotone and Lipschitz continuous operator, as well as the fixed point problem in real Hilbert spaces with a ρ-demicontractive mapping. These inertial-type iterative methods use self-adaptive step size rules that do not require previous knowledge of the Lipschitz constant. We also show that the proposed methods strongly converge to a solution of the variational inequality and fixed point problems under appropriate standard test conditions. Finally, we present several numerical examples to show the effectiveness and validation of the proposed methods. Full article
(This article belongs to the Special Issue New Advances in Functional Analysis)
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20 pages, 348 KiB  
Article
New and Improved Criteria on Fundamental Properties of Solutions of Integro—Delay Differential Equations with Constant Delay
by Cemil Tunç, Yuanheng Wang, Osman Tunç and Jen-Chih Yao
Mathematics 2021, 9(24), 3317; https://0-doi-org.brum.beds.ac.uk/10.3390/math9243317 - 20 Dec 2021
Cited by 12 | Viewed by 1918
Abstract
This paper is concerned with certain non-linear unperturbed and perturbed systems of integro-delay differential equations (IDDEs). We investigate fundamental properties of solutions such as uniformly stability (US), uniformly asymptotically stability (UAS), integrability and instability of the un-perturbed system of the IDDEs as well [...] Read more.
This paper is concerned with certain non-linear unperturbed and perturbed systems of integro-delay differential equations (IDDEs). We investigate fundamental properties of solutions such as uniformly stability (US), uniformly asymptotically stability (UAS), integrability and instability of the un-perturbed system of the IDDEs as well as the boundedness of the perturbed system of IDDEs. In this paper, five new and improved fundamental qualitative results, which have less conservative conditions, are obtained on the mentioned fundamental properties of solutions. The technique used in the proofs depends on Lyapunov-Krasovski functionals (LKFs). In particular cases, three examples and their numerical simulations are provided as numerical applications of this paper. This paper provides new, extensive and improved contributions to the theory of IDDEs. Full article
(This article belongs to the Special Issue New Advances in Functional Analysis)
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21 pages, 342 KiB  
Article
A General Class of Differential Hemivariational Inequalities Systems in Reflexive Banach Spaces
by Lu-Chuan Ceng, Ching-Feng Wen, Yeong-Cheng Liou and Jen-Chih Yao
Mathematics 2021, 9(24), 3173; https://0-doi-org.brum.beds.ac.uk/10.3390/math9243173 - 09 Dec 2021
Cited by 10 | Viewed by 1588
Abstract
We consider an abstract system consisting of the parabolic-type system of hemivariational inequalities (SHVI) along with the nonlinear system of evolution equations in the frame of the evolution triple of product spaces, which is called a system of differential hemivariational inequalities (SDHVI). A [...] Read more.
We consider an abstract system consisting of the parabolic-type system of hemivariational inequalities (SHVI) along with the nonlinear system of evolution equations in the frame of the evolution triple of product spaces, which is called a system of differential hemivariational inequalities (SDHVI). A hybrid iterative system is proposed via the temporality semidiscrete technique on the basis of the Rothe rule and feedback iteration approach. Using the surjective theorem for pseudomonotonicity mappings and properties of the partial Clarke’s generalized subgradient mappings, we establish the existence and priori estimations for solutions to the approximate problem. Whenever studying the parabolic-type SHVI, the surjective theorem for pseudomonotonicity mappings, instead of the KKM theorems exploited by other authors in recent literature for a SHVI, guarantees the successful continuation of our demonstration. This overcomes the drawback of the KKM-based approach. Finally, via the limitation process for solutions to the hybrid iterative system, we derive the solvability of the SDHVI with no convexity of functions u↦fl(t,x,u),l=1,2 and no compact property of C0-semigroups eAl(t),l=1,2. Full article
(This article belongs to the Special Issue New Advances in Functional Analysis)
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